Question

prime factorisation of (-2744000)

Answer 1

(ii) On factorising 2744000 into prime factors, we get:

2744000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 7 x 7 x 7

On grouping the factors in triples of equal factors, we get:

2744000 = {2 x 2 x 2} x {2 x 2 x 2} x {5 x 5 x 5} x {7 x 7 x 7}

It is evident that the prime factors of 2744000 can be grouped into triples of equal factors and no factor is left over. Therefore, 2744000 is a perfect cube. This implies that – 2744000 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get: 2 x 2 x 5 x 7 = 140

This implies that 2744000 is a cube of 140. Thus, – 2744000 is the cube of – 140.

Answer 2

$\begin{array}{r|1}2&2744000\\ \:\: \cline{2-2}2&1372000 \\ \cline{2-2}2&686000 \\ \cline{2-2}2&343000\\ \cline{2-2}2&171500 \\ \cline{2-2}2&85750\\ \cline{2-2}2&42875 \\ \cline{2-2}5&8575 \\ \cline{2-2}5&1715 \\ \cline{2-2}7&343 \\ \cline{2-2}7&49 \\ \cline{2-2}7&7\\ \cline{2-2}&1 \\ \end {array}$